Question: Solve for $x$ and $y$ using substitution. ${-6x+3y = 12}$ ${y = -3x-11}$
Solution: Since $y$ has already been solved for, substitute $-3x-11$ for $y$ in the first equation. ${-6x + 3}{(-3x-11)}{= 12}$ Simplify and solve for $x$ $-6x-9x - 33 = 12$ $-15x-33 = 12$ $-15x-33{+33} = 12{+33}$ $-15x = 45$ $\dfrac{-15x}{{-15}} = \dfrac{45}{{-15}}$ ${x = -3}$ Now that you know ${x = -3}$ , plug it back into $\thinspace {y = -3x-11}\thinspace$ to find $y$ ${y = -3}{(-3)}{ - 11}$ $y = 9 - 11$ $y = -2$ You can also plug ${x = -3}$ into $\thinspace {-6x+3y = 12}\thinspace$ and get the same answer for $y$ : ${-6}{(-3)}{ + 3y = 12}$ ${y = -2}$